Category: Graphs & Graphics

For those who require a graphical representation of concepts.

Hierarchy of Shapes

Duncan Leave a comment

Abraham Maslow’s hierarchy of needs is a concept often used by the mildly educated to assert intellectual superiority over common folk. The idea is simple enough for a first year college student to grasp while complex enough to confound ignorant laborers.

It was Abe’s observation that human needs could be classified into five distinct categories: health, safety, love and belonging, esteem and self-actualization. He observed that as the more basic needs, such as oxygen, food and safety, are satisfied, one shifts attention to more advanced needs, such as relationships, art and philosophy.

Self-actualization could be described as the desire of humans to achieve their full potential. Although most people associate Maslow with self-actualization, the term was actually created by Kurt Goldstein. This is an example of Stigler’s law, which states that inventions are often named after the one who popularized it, not the one who discovered it. Although most people associate Stephen Stigler with Stigler’s Law, the concept was actually discovered by Robert K. Merton. This is an example of Stigler’s law.

Aside from the irony of the inauthenticity of the perceived origin of self-actualization, another interesting facet of Maslow’s hierarchy is that it is often represented by a pyramid or triangle, though Maslow never used these shapes to illustrate his idea. The reason why a triangular shape is used to describe the progression from the basic deficiency needs to more complex being needs is that Maslow’s arrangement is not only chronological, but hierarchical. This means that the needs at the bottom not only precede those at the top, they are also less significant.

The triangle is the elitist’s favorite shape. Those who crave success and exclusivity maintain a triangular view of society, for it is the perfect geometrical manifestation of elitism. The wide base of the triangle represents the ignorant masses, toiling in bowels of obscurity, while the narrow peak symbolizes the exclusive few who, from their lofty vantage, hold the keys to truth and happiness. The orientation of the shape is also significant, for the transition from the hungry and poor to the self-actualized is one of upward ascent, which implies progress.

There are much more inclusive shapes one can choose to represent an idea. The square, for example, may possess four distinct and harsh corners, but it does not lend itself to any one side and is equally inclusive at the top as it is at the bottom. Likewise, the circle, with its smooth, noble perimeter, promotes wholeness and equality, paying no mind to orientation.

Don’t trust anyone who shows you a triangle.

The Show Piece

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Gum chewing is a strange thing. It gives us flavor without nourishment, confusing our stomach. It also exercises our mandibles and gives talkative people something to do when there’s no one around to listen, for as the crying infant has the pacifier, the ceaseless speaker has chewing gum.

Modern chewing gum packaging often consists of an outer package which contains all of the graphics and production information and an inner package which holds the gum in neat little compartments – neat little compartments of chaos.

The inner package is visible through a semi-circular cleft in the outer cover. By firmly grasping the revealed section with the thumb and index guy, we can slide the internal package out, gaining access to its luscious innards. Besides granting quick access to the product, the opening in the outer package serves a second, more important function that is often ignored.

If we wanted to know whether the package was empty, we could slide the inner section out and take a look or we could save ourselves seconds of agony and use the opening to view the show piece.

The show piece is the single piece of gum visible through the outside packaging. If we simply eat the show piece last then we must never again endure the disappointment of opening an empty pack.

When you chew your gum, do you eat the show piece last?

Official Opposition

Duncan Leave a comment

Despite how insightful the idea may seem, the opposite of love is not indifference. The opposite of something isn’t nothing, it’s something that is opposed or contrary to it. If the opposite of love is indifference, then the opposite of every emotion must also be indifference. Though cold is technically the absence of heat, the opposite of a high temperature is a low temperature, not a mild temperature. So what are opposites, exactly, and how do we determine their identity?

Although we all understand what an opposite is, defining it is a little tricky. For example, everyone knows that the opposite of evil is good and that good triumphs over evil, but how do we define good in relation to evil? Good is not merely the absence of evil, neither is it something totally dissimilar; it is the inverse, the nemesis or, expressed mathematically, evil*-1.

There are actually two distinct variations of opposites: polar opposites and binary opposites. Examples of polar opposition would include an inch and a mile or constipation and diarrhea, because they reside at different ends of a spectrum. Polar opposites are simply the inverse of each other and usually aren’t very difficult to discern.

Binary opposites, however, are not commonly identified as part of a spectrum, but are defined in relation to a counterpart. Men and women, for example, are opposites not because they are contrary or inverted, though in some ways they are, but because they make up the gender binary. Using this interpretation, the opposite of night would be day and the opposite of a hand would be a foot.

Sometimes a subject may have more than one binary opposite. Although this seems nonsensical, we must remember that most things can be categorized in different ways. For example, a man is not merely defined as one of two sexes, but as a human, an intelligent being, a creature, a collection of organic matter, an imperfect being, a creator, a destroyer and an explorer. So depending on the context, the opposite of a man could be an animal, an inanimate object, an angel, demon, god or ghost, a force of good or a force of evil. Likewise, the opposite of a chicken could be an egg, but the opposite of a chicken stir fry would probably be a beef stir fry.

Now what happens when we add attributes to the subject? A tall man is an example of something that has both a polar and binary opposite.

Tall Man
Tall Woman
Short Man
Short Woman

Here we see the different potential opposites of a tall man. The opposite of the subject, man, is woman, and the opposite of the attribute, tall, is short. So how do we determine the opposite of a tall man, since it’s comprised of two components?

There are three dominant theories which dictate how we derive the opposite in a case such as this. The first is opposite subject theory, which states that we should find the inverse of the subject, resulting in tall woman. The second is known as opposite attribute theory, and it requires us to invert only the attributes, which produces short man. The third theory is called complete opposite theory, and it states that we must find the opposite of both the subject and the attribute(s), giving us short woman.

One idea that has fallen out of favor in recent years is opposite attraction theory, which uses the laws of attraction to deduce opposites. This theory is very fun and works great in the realms of romance, positive thinking and electromagnetism, but it doesn’t help much in our case. Each of our three dominant theories has its own strengths and non-strengths, which we will be revealed through examination our next example: a baby boy playing. Let’s see how each of our theories decodes the opposite in this scenario.

Baby Boy Playing
Baby Boy Working
Baby Girl Playing
Baby Girl Working
Adult Boy Playing
Adult Boy Working
Adult Girl Playing
Adult Girl Working

Opposite subject theory would have us invert the subject, boy, resulting in baby girl playing. This theory works very well when dealing with subjects with obvious polar or binary opposites, but what about something that doesn’t have a clear opposite, like a paperclip, cloud or dishwasher?

The second option simply asks us to invert all of the described attributes, leaving only the subject unchanged, which gives us adult boy working. For a long time this theory worked fine and the land was green and good, until the crystal cracked.

A fringe theory broke off from opposite attribute theory, and it asked us to find the primary attribute of the subject and invert only that attribute. In this case, the primary attribute would be baby, since it most intrinsically and decisively defines the subject, boy, so we would get adult boy playing.

The difficulty with primary attribute theory is discerning which attribute is primary and whether or not it’s actually part of the subject. Some might argue that the primary attribute in this case is boy and that the subject is actually baby, but the term baby is more commonly used as an adjective to describe things like baby food, baby clothes, baby steps and baby baboons.

However, a big blue fish has two seemingly equal defining attributes. This means that there is either no correct opposite or a number of equally correct opposites, which may cause one to question the existence of moral absolutes.

The third option, complete opposite theory, would have us invert both the attributes, baby and playing, as well as the subject, boy, which produces adult girl working. Although this answer is very convincing, it gives us a result that is totally dissimilar to the original. This method is surely logical, but it breaks down when we apply it to certain well-known opposites.

We all know the opposite of walking forward is walking backward, not running or crawling backward. We also know that the opposite of a human getting older is a human getting younger, not a non-human getting younger. This is because opposites must share a point of reference, which is usually the subject. If they don’t, then we end up with two things that are totally different, which is not what opposites are about. This method also suffers from the same problem as opposite subject theory, since both require the subject to be inverted.

Now let’s take a look at both of the types of opposites as well as each of the theories we explored. In order to help us understand opposites more clearly, let’s use mathematic expressions for both polar and binary opposites with each of the theories applied.

Expression Polar Opposite
Subject Attribute(s) Primary Attribute Complete
x -x Not Applicable Not Applicable -x
x+1 -x+1 x-1 x-1 -x-1
5x-5 5(-x)-5 -5x+5 -5x-5 -5(-x)+5
1(-x+1)^-1 1(x+1)^-1 -1(-x-1)^1 1(-x+1)^1 -1(x-1)^1
Expression Binary Opposite
Subject Attribute(s) Primary Attribute Complete
x y Not Applicable Not Applicable y
x+1 y+1 x+0 x+0 y+0
5x-5 5y-5 5x-5 5x-5 5y-5
1(-x+1)^-1 1(-y+1)^-1 0(-x+0)^0 1(-x+1)^0 0(-y+0)^0

As we can see, we get very different answers depending on how we go about getting our opposites. And even when we use numbers, opposites are not easily determined. Although in these examples we can simply use the order of operations to determine the primary attribute, we still run into difficulty with multiple operations of the same order.

It’s easy to see that the polar opposite of x is -x, and the binary opposite is y. Likewise, the polar opposite of 1 is obviously -1, and the binary opposite is even more obviously 0. However, while the polar opposite of 5 is clearly -5, there is no binary opposite to such a number. Just like dishwashers and many other real-world examples, most numbers don’t have binary opposites, which means we must use the polar opposite, since the alternative could mean inverting nothing at all. Now we see that no opposite type or theory is fully adequate, since they all have exceptions.

So how do we know when to use polar opposites and when to use binary opposites? Determining the opposite of an attribute is relatively simple, since adjectives usually fall on a spectrum. For subjects, however, one tactic we can use is to test for an obvious binary opposite before exploring polar opposites. Since not all subjects have a binary opposite, it would make sense to first test to see if it has a well-known counterpart.

Now which theory is most versatile and consistently produces meaningful opposites? Opposite subject theory can force us to conjure up ridiculous nonexistent beings or mechanisms to find an opposite, and opposite attribute theory can produce results that are too dissimilar to be recognized as an opposite. Complete opposite theory, while perhaps the most logical, suffers from both of these complications. Opposite primary attribute theory, on the other hand, allows us to avoid silly subject opposites and also yields recognizable and meaningful opposites.

So how do we resolve subjects that have multiple attributes but no primary attribute? In other words, what if our adjectives aren’t cumulative? Well, just as a subject may have more than one opposite, there can also be more than one opposite when there is no primary attribute. If both attributes are equally describe the subject, a wise strategy would be to choose the one that is most easily inverted. This would turn our big blue fish into a small blue fish, since it’s much simpler to determine the opposite of big than blue. If one attribute is not easier to invert than another, then it may be acceptable to invert both or all of the attributes.

But sometimes one of the attributes, though just as significant or even more significant than the others, just doesn’t make sense when inverted alone. So if we had to find the opposite of a generous friend giving money, it wouldn’t be a selfish friend lending money. A generous friend taking money doesn’t make much sense either. It would be best to invert both generous and giving, making this person a selfish friend taking money, which makes a lot more sense.

Some people have difficulty just identifying attributes of a subject, let alone determining which one to invert. This is because attributes are not equal to adjectives. Attributes are features or characteristics of the subject. In the example above, a generous friend giving money, generous is obviously one of the attributes of friend, but what about giving money? The term giving is not an attribute on its own, and neither is money, for if we separate them, then there are two subjects: friend and money. No, in this case giving money is the second attribute of friend, because we all know that the opposite of giving money is taking money, not taking non-money. In a way, each attribute is treated as its own separate opposite before being tested against any other attributes and then applied to the original subject.

The only other obstacle that runs this theory ashore is a subject with no describing attributes. In these cases, we can defer to opposite subject theory, since that is the only remaining solution. Now let’s see how it works.

Original Opposite(s) Explanation
A Chicken An Egg No attributes, invert subject. Chicken and egg are binary opposites.
Sea Land Sky No attributes, invert subject. Sea, land and sky are binary opposites.
A Giant Chicken A Tiny Chicken Giant and tiny are polar opposites.
A Skilled Carpenter A Clumsy Carpenter Skilled and clumsy are polar opposites.
An Emotional Romance Movie A Dull Romance Movie Cumulative adjectives. Emotional is easier to invert than romance.
A Beautiful, New House An Ugly, New House A Beautiful, Old House An Ugly, Old House Coordinate (independent) adjectives. No primary attribute.
A Shy Girl on a Blind Date An Outgoing Girl on a Blind Date Shy is the primary attribute. Shy is easier to invert than on a blind date.
A Horrible Disease That Kills Quickly A Horrible Disease That Kills Slowly Horrible is the primary attribute, but inverting it doesn’t make sense.
A Strong, Handsome Hero A Weak, Hideous Hero A Strong, Hideous Hero A Weak, Hideous Hero Coordinate (independent) adjectives. No primary attribute.
An Honest Lawyer Telling the Truth A Dishonest Lawyer Telling Lies Honest is the primary attribute, but inverting it alone doesn’t make sense.

As we can see, the answer largely depends on context. It seems strange that the opposite of a chicken is an egg while the opposite of a giant chicken isn’t a giant egg. However, if our attribute was friendly, rather than giant, then it would seem silly to invert the subject, since eggs are hardly friendly at all.

Likewise, it would appear to many that the opposite of a strong, handsome hero must be a villain, since they could be considered both polar and binary opposites. But again, inverting the subject is only tempting in these situations because there is an obvious opposite to the subject. If it was a Russian farmer who was strong and handsome, then we would be much less inclined to find the subject’s opposite. As a final example of opposites, let’s consider the case of one of the most popular comic book heroes of all time: Superman.

Superman has faced many foes over the years, including cyborgs, monkeys, millionaires, thieves, ghosts, gods, demons, environmentalists, Kryptonians, scientists, magicians, aliens and many others. Although Superman has handled a wide variety of villains, some of them are more memorable than others. This is because a good villain is the antithesis of the hero, standing against what the hero stands for and embodying virtues that oppose those of the hero. Most heroes have an archenemy or nemesis, which is usually a being who is their perfect opposite.

Although many would identify Lex Luthor as Superman’s nemesis, there have been several attempts to create an evil counterpart to the Man of Steel. Ultra-Humanite, Lex Luthor, Ultraman and Bizarro were all made with the intent of producing a villain who is completely contrary to Superman, but did any of them really succeed?

These four foes basically fall into two categories: the ones with superpowers and the ones without. Ultraman and Bizarro have similar or identical physical powers to those of Superman, such as flight and super-strength, while Ultra-Humanite and Lex Luthor have only increased intellectual abilities. Ultra-Humanite even possesses a crippled body, which was meant to make him a more complete opposite of Superman.

Also, in Kill Bill: Vol. 2, David Carradine’s character argues that the antithesis of Superman is actually Clark Kent – a cowardly, benign human with no interest in helping or hurting others. So which one of these characters is the true opposite of Superman? Let’s take a look at each of them and see whether they are using polar or binary opposites and which opposite theories are being applied.

Character Features
Strength Intelligence Super Powers Personality
Superman Super Normal Flight, Heat Vision, Freeze Breath, etc. Selfless, Humble, Honest
Ultra-Humanite Limited Super None Selfish, Insane, Hateful
Lex Luthor Normal Super None Selfish, Ambitious, Deceitful
Ultraman Super Normal Flight, Heat Vision, Freeze Breath, etc. Selfish, Ambitious, Deceitful
Bizarro Super Limited Flight, Freeze Vision, Flame Breath, etc. Confused
Clark Kent Normal Normal None Disengaged, Timid, Fearful

As we can see, each villain has its own approach to opposing Superman’s features. Ultra-Humanite and Lex Luthor mirror Superman’s incredible physical abilities with intellectual abilities, since they are binary opposites, with Ultra-Humanite’s inferior physical strength representing a polar opposite. In the same way, Bizarro’s limited intelligence is an attempt to mirror Superman’s normal intelligence, though also serving to separate him from other villains. Instead of contrasting Superman’s physical abilities, Ultraman and Bizarro share Superman’s powers, but some of Bizarro’s abilities are actually inverted from those of Superman.

As far as personality and behavior goes, Bizarro again separates himself from the pack with a lack of obvious maniacal intent. Superman is good, and the opposite of good is evil, so it would make sense to have an evil nemesis. But Bizarro, like the other villains, is a combination of opposite types and theories, so it’s likely that his creators were merely attempting to make a character who was extremely dissimilar to Superman in all respects. Unfortunately this doesn’t explain why Bizarro flies instead of digging and why he isn’t physically weak like other villains.

Clark Kent, on the other hand, embodies not the opposite of Superman’s features, but the absence of them. And, as we already discussed earlier, the opposite of something is not nothing. If Clark Kent was the opposite of Superman, then he would also be the opposite of Lex Luthor, Bizzaro and any other extraordinary character.

Of all of Superman’s Enemies, Bizarro is the most obvious attempt to create a complete opposite. Bizarro’s creators even went to so far as to give him the ability to see a short distance behind his head, which is supposed to be the opposite of Superman’s ability to see a great distance in front of him. Although they obviously went to great length to ensure that Bizarro was the complete opposite of Superman, they ultimately failed. This is because there can be no true complete opposite of something with as many characteristics as a person, especially when we know so much about them.

Superman is not just a Superhero with superpowers, he’s an alien, an idealist, a person of moderate height and intelligence, he’s brave, friendly, helpful and good-looking, he has short, dark hair, he’s not an amputee or a football player, he never gets sick, he can see, smell, taste, touch and hear, he’s emotionally stable, he sleeps in a bed and so on.

This is why complete opposite theory and opposite attribute theory can’t work: there are too many characteristics to invert. As we already discussed, the best way to find the opposite of something is to invert its primary attribute or attributes, so we need to ask ourselves what are the most defining features?

Well, since Superman is the only Kryptonian on Earth, that would be a good place to start. He also possesses incredible physical powers that other people do not, and he’s a hero who has dedicated himself to defending Earth and its inhabitants from evil. What’s the opposite of a physically powerful alien selflessly protecting others? Probably an intellectually powerful human selfishly exploiting others.

Terminal Velocity

Duncan Leave a comment

In the year 2000 there were over six million motor vehicle accidents in the United States, resulting in 41,945 human fatalities. In that same year an estimated 247,000 deer were maimed or killed in motor vehicle collisions, and it’s likely that other species, such as birds, suffered even greater losses. Driving is undeniably dangerous.

Many of these accidents were likely caused by intoxication or carelessness, but piloting a 1,000 kg metal box at speeds exceeding 100 km/h is inherently hazardous. In an effort to mitigate the number of vehicle collisions, some groups are lobbying for reduced speed limits, especially in residential and high-traffic areas. Their premise that slower vehicles will produce fewer collisions couldn’t be less inaccurate.

It’s obvious to most that slower vehicles are safer, since the force of impact is diminished and the window for driver reaction is expanded. Objects with no velocity are the easiest to avoid since they rarely crash into things. Unfortunately, getting motorists to slow down is not as simple as a mere adjustment in signage.

A report by the Turner-Fairbank Highway Research Center concluded that neither lowering nor raising speed limits by up to 24 km/h had a significant effect on motorist speed. The report’s conclusion states, “…motorists do not alter their speed to conform to speed limits they perceive as unreasonable for prevailing conditions.” But even if drivers did obey the new speed limits, a more challenging question must be answered: how many lives are we willing to sacrifice?

Most groups advocating lower speed limits are requesting that they be reduced by 10 or 20 km/h, but slower vehicles would still produce some collisions, injuries and deaths. So how many fatalities are we willing to accept as a natural consequence? This is a very difficult question to answer, and it applies to many areas beyond that of motor vehicles.

In every industry there are deaths, injuries or accidents of some kind. Rules are created, precautions are taken and laws are passed to reduce these incidents, but they aren’t really aimed at reducing the number of incidents to zero. This is because safety is inversely proportional to efficiency.

Imposing health and safety practices on an industry will inevitably make it less efficient. Conversely, an industry operating without any concern for safety would likely be very efficient, that is, until its workforce is deceased or debilitated.

Some concerned individuals feel a moral obligation to avoid purchasing products from companies that exploit people, animals or the environment, but again, how much is too much? Let’s look at some examples of absolute positions often taken on subjects that are not absolute.

Many people hold a negative view of oil companies because of the environmental damage they inflict, so they ride a bicycle or take public transit. But almost all the products they buy are transported by fuel-burning freight and constructed with oil-based synthetic materials.

Some individuals choose not to eat meat so that animals might be spared unnatural suffering and an early death, but many animals are killed by farming machinery during the harvest of crops and even more are displaced by agricultural properties. And, of course, they are not concerned with the number of insects that are crushed beneath their feet every day, since bugs do not hold a high animal value.

The idea that moral issues are not as dry and cut as we might like can make us feel overwhelmed and impotent. When we realize that no person, organization or action is purely good or evil, we can succumb to what is known as the grey escape – an apathetic exit to a moral predicament. The grey escape is the perception that when an issue is complex or its answer is not easily reached, the solution must be either nonexistent or unworthy of investigation. People who subscribe to this line of thinking are often too concerned with entertainment, success and pleasure to bother the moral and abstract. “Because the matter is grey,” they say, “it deserves not the time of day.”

Grey things are the most important.

Descent

Duncan Leave a comment

If you’ve ever watched a science fiction show, such as Star Trek or Babylon 5, then you likely find the idea of space travel very intriguing. Imagine stars streaking past your solar windshield as your ship comfortably cruises from world to world in a matter of hours. But aside from the technological and physical impossibilities of such travel, there is another limitation which ensures that we will never command a Galaxy-class starship: our dimensional perception.

In the world of Star Trek, whenever two ships encountered one another, they would always be aligned to the same axis. This makes sense to us because in classical flight, which takes place on Earth, all soaring vessels are tethered to the ground by gravity, requiring that they be oriented in a unified manner to combat this force. In space, however, there is no gravity or pole to which we can reference our orientation, so there’s no reason why two ships should be aligned the same way when they meet. But we aren’t here to poke black holes in classic works of science fiction, however entertaining that might be, we’re here to find out why we aren’t fit for duty in the Federation.

We live in a three dimensional world, but we do not interact with all three dimensions equally. The prime dimensions of our experience are the x and z axes because they are the ones in which we move the most freely. We scarcely travel up or down, except to reach another horizontal plane on which we can interact. Even fish and birds, though they move up and down freely, experience the world in the same way we do, for their bodies must remain aligned in relation to the Earth.

Our bodily systems of digestion and circulation are also intended to function most effectively when our bodies are properly oriented with the ground beneath our feet. In addition, our eyes are engineered to take in a wider range of horizontal information than vertical, converting that information into a two-dimensional mental image. Likely because of our upbringing in a world dominated by two dimensions, and the nature of vision itself, our imagination is conditioned to perceive the world in this way. When we imagine a location, we do not imagine a three-dimensional rendering of that place, but merely a two-dimensional picture. This is why maps are drawn from a top-down view – the y-axis just isn’t as relevant to our experience. Another reason could be that we have traditionally used use two-dimensional means of communicating images, such as drawing on paper, which only allow us to effectively portray two dimensions at a time.

To illustrate the difficulty in interpreting space this way, let’s take a look at some grids plotting three three-dimensional points.

Here’s what it would look like if we combine these grids into one three-dimensional chart:

Try to solve for the position of the three points in the final grid of the image below.

Our two-dimensional approach to spacial interpretation makes us totally unfit for life in space, where free movement and rotation is available in all three dimensions. This has been proven by the limited success of video games which feature six degrees of freedom, such as Star Luster and the Wing Commander series. Though many of these titles are ingenious in concept and design, gamers found themselves both astonished and confounded by total planar liberation. Many developers have abandoned such design in favor of a two-dimensional interpretation of space travel, where vessels maintain a consistent, unified orientation.

Behold, the Earth from a perfectly legitimate perspective:

Whether engaging in a starship dogfight, navigating an asteroid field or simply plotting a leisurely interstellar cruise, those of us raised on the surface of a planet are dangerously unqualified for such tasks. It is possible that we could be conditioned through the use of holograms and flight simulators, to interpret our surroundings in a manner consistent with the demands of space travel. If that didn’t work, raising children in space could enable them to comprehend and navigate three dimensions quite easily, but there’s only one way to find out, NASA.

Lex Talionis

Duncan Leave a comment

Crime is an inevitable part of our world. No matter how much freedom and plenty are available inside the fence, some people will inevitably climb that fence, either due to boredom, curiosity, selfishness or mental impairment. Though we may be able to reduce crime through social programs and education, the question remains: what do we do with those who break the law?

Throughout history this question has been answered in many different ways, including fines, hard labor, torture, mutilation, exile, execution and incarceration. Imprisoning convicts has become the established method of administering punishment in the developed world, where physical discipline is considered barbaric. Of course, it is likely that a society which used beatings and public shaming to punish its criminals might consider the idea of removing people from their belongings, friends and family for decades to be much more brutal.

Incarceration is a luxury that many societies have not been able to afford, and many questions have been raised about the how correctional the facilities actually are. British Politician Douglas Hurd, regarding the effectiveness of incarceration, stated that, “prison is an expensive way of making bad people worse.”

Each society has its own view of law and criminal justice which defines what behavior is considered criminal, which crimes are, in general, grievous and the aim of punitive action. No matter what the method of punishment, the intent behind criminal justice is to satisfy one or more of four major objectives:

  1. Retribution: To exact punishment on the person who committed the crime.
  2. Deterrent:  To set an example to the rest of society in the hopes of discouraging others from similar activity.
  3. Protection: To keep the citizens safe from criminals.
  4. Correction: To ensure that criminals do not continue to offend.

Different methods of punishment accomplish these four objectives in different ways, as illustrated by this chart:

Objective Punishment
Pain Mutilation Fines Exile Incarceration Execution
 Retribution Strong Strong Strong Strong Strong Unknown
 Deterrent Fair Strong Fair Strong Fair Strong
 Protection Weak Strong Weak Strong Strong Very Strong
 Correction Weak Strong Weak Weak Fair Very Weak

Obviously the level to which each type of punishment achieves its aim depends on implementation. Incarceration, for example, provides a great opportunity for corrective programs as well as negative influence from fellow criminals, while mutilation, which may prevent future crime, can render recipients permanently debilitated. The method of punishment which consistently generates the most controversy is execution.

The death penalty holds the most absolute consequences of any punishment, which is what makes it so attractive to its supporters and so unbearable to its detractors. Although execution grants permanent protection from further crime, critics argue that because death is irreversible we cannot offer compensation to the wrongfully convicted. This argument is based on several unprovable presumptions. First, that every wrongfully convicted individual will be exonerated, second, that those who are exonerated are, in fact, innocent and finally, that we can adequately compensate for incarceration. It’s true that we cannot revive the dead, but neither can we travel back in time to restore lost years to these whose lives we have ruined.

There is much debate over whether increased punishment leads to increased deterrence. As we have already discussed, there is at least a meaningful relationship between punishment and deterrence, which means that the death penalty would offer the greatest deterrence of any form of punishment. So capital punishment offers impenetrable protection, tenacious deterrence and non-existent correction, but how does it fair at dispensing retribution? Death penalty supporters often tout its retributive power, but we can’t actually be certain how effective it is.

By incarcerating an individual we can control almost all aspects of their lives, but when we kill someone we relinquish control of their fate to the icy coils of death. Sure, there’s the fear and mental anguish endured by those poor souls on death row, but what happens after they die and how can we be sure that it’s bad?

There are many theories and beliefs about what awaits us beyond the grave, including heaven, hell, Blisstonia, non-existence, parallel realities and reincarnation, but ultimately we don’t know what exactly happens in the afterlife because scientists stubbornly refuse to die and study it.

If the criminal were to go to heaven or a parallel world after death, then there wouldn’t be much of a punishment. Non-existence seems frightening, but we all had no problem not existing before we were born, so it can’t be that bad. If we only had some evidence that there was, in fact, eternal torture awaiting the victim, then capital punishment might be viable. But as it stands, there’s a chance that they could end up in paradise, and death shall have no dominion.

Dice

Duncan Leave a comment

There is an explanation for everything. Our world is comprised of matter and energy that behaves in predictable ways, allowing us a degree of certainty when imagining hypothetical situations. Yet, despite the massive leaps forward in science, we occasionally find ourselves in the midst of events so absurd, so seemingly unpredictable, that we can only respond with the words, “well, that was random.”

It wasn’t.

Although we may not have been able to predict such scenarios, they weren’t random; they only seemed random because we didn’t know why it occurred. There’s likely a perfectly legitimate explanation for the any situation we find ourselves in, no matter how strange. Before we continue, let us make some important declarations and distinctions about how the universe operates:

  1. Nothing is random, because everything has a cause.
  2. Some things are pseudo-random, having a nearly incomprehensible cause.
  3. Some things only seem random, but actually maintain a comprehensible cause.

Although no occurrence can be truly random, by categorizing all measurable events as either pseudo-random or seemingly random, we may better understand what is meant when something is characterized as random. First, let’s deal with those things that we might consider random, but which are actually just unpredictable.

Random number generation has been used throughout history for many purposes, most notably gambling. By creating devices that use high speeds and complex vectors, such as dice or roulette wheels, we can produce outcomes which cannot be predicted, at least not with the human eye. More recently, we have used computers to generate pseudo-random numbers using algorithms and seed values. Though much more elaborate than physical random number generation, the results are still derived from a concrete source, so they cannot be truly random.

A popular example of perceived randomness, often used to prove some point about the universe, is the idea that an infinite number of monkeys on an infinite number of typewriters will produce the complete works of Shakespeare. The premise being that the typing pattern of monkeys is random and, therefore, it will eventually produce every outcome. This is not true.

Monkeys will never produce the works of Shakespeare, and we don’t need to lock a monkey in a room with a typewriter to find that out. If we were to simply imagine the result of such an experiment, we would likely conclude that the monkey had been hitting keys randomly, but this is not the case. The mind and motions of a monkey are not random, they follow a pattern. Much like the roll of a dice, we might not be able to predict the outcome, but there is most certainly a pattern, and it is most certainly different from the pattern found in Shakespeare. If we were so inclined, we could observe and record the results of monkey typing on a massive scale and eventually produce some algorithm which would describe the most commonly used keys, key combinations and punctuation. For all we know, it’s possible that monkeys might detest pressing the Q key and avoid touching it at all costs, or maybe they would continuously press the Home key in a depressing attempt to communicate their longing for freedom.

Now let’s discuss the second type of event, which includes those things that might seem random, but are actually quite predictable. It is possible that rolling dice might belong in this category, for if we were watch the roll in slow-motion or merely increase the size of the dice, the outcome would be much more predictable. Also, rolling a dice on a smooth surface makes the process less complex and, thus, further from the unattainable state of randomness.

Benford’s law is another example of finding a predictable pattern where we would typically expect randomness. In 1881, Simon Newcomb, a bearded man, observed a peculiar statistical phenomenon. While spending a relaxing evening beside the fire, sipping a glass of wine and thumbing through logarithm books (as all of us do), Newcomb noticed that the pages which contained numbers that started with the number 1 were more worn than other pages. He then analyzed a variety of different data sources and found the same anomaly, but his discovery was largely ignored until it was verified years later by similar examinations of data.

Basically, Benford’s law says that if we examine data from almost any source, we will find a definitive pattern in the value of the first digit of those numbers. The most frequent number is 1, which is found to be the left-most digit in a staggering 30.1% of data values. The frequency of each number decreases as we approach 9, which appears as the first digit a mere 4.6% of the time. Benford’s law can be used to detect tax fraud, since forged numbers contain a more even distribution in first-digit frequency.

Unusual behavior is much easier to predict than a dice roll, for it can often be traced back to previous experiences, trends and habits. In fact, these events are not at all difficult to predict; they are merely unexpected. If we were to attempt to prove the existence of randomness by, for example, saying a random word, the word would be inevitably predictable. The process of choosing that word would merely be a brief expedition into the subconscious – nothing more. After blurting out the unchosen word, one would likely need only to probe recent memory to find its inception.

Go ahead, try to say something random.